2 y ' ' x y ' 3 y=0 .
(5 Points) Find the recurrence relation for the coefficients of power series solutions about the point x=0 that satisfy the ODE, using the power series method. (10 Points) Find two power series solutions of the ODE, about the point x=0 , such that one satisfies y 0=1 with y ' 0 =0 and the other one satisfies y 0=0 with y ' 0 =1 . It is sufficient to state only the first four nonzero terms in each series.